The surveys show only tepid support for building the wall, an oft-repeated Trump campaign promise that he sees as an essential part of his appeal. Forty-three percent of voters want to construct the barrier, while 55 percent do not, according to the Quinnipiac survey. Only 39 percent of Americans favor building a wall along the entire U.S. border with Mexico, while 56 percent oppose the project, according to the CNN poll. Meanwhile, the Post/ABC survey found 42 percent back building the barrier, while 54 percent oppose the plan.
As the shutdown drags on, Trump has tried to shift the blame to Democrats, who control the House and can block funding legislation in the GOP-held Senate. In a tweet Monday morning, he argued Pelosi and Senate Minority Leader Chuck Schumer "can end the shutdown in 15 minutes," contending the closure "has become their, and the Democrats, fault!"
Pelosi responded by saying "it's time for you to stop standing in the way of re-opening the government." She again called on the president to urge the Senate to approve House-passed bills to end the shutdown, which Trump has threatened to veto. Pelosi included a video from a December meeting in which the president told Schumer he would be "proud to shut down the government for border security" and "take the mantle" if funding lapsed.
It is unclear if an extended shutdown that causes more damage to government workers and services will change political strategy. Those who oppose the wall are torn about whether Democrats should compromise to reopen the government, according to the Post/ABC poll. Forty-eight percent of respondents who do not want a border wall say Democrats should refuse to fund the barrier even if the closure continues, while 45 percent think the party should make a deal.
A spokesman for Pelosi did not immediately respond to a request to comment on what it would take for Democrats to give ground and make a deal. In a speech on the Senate floor on Monday, Schumer said that giving in to Trump's demand for the wall would encourage the president to use similar tactics in the future.
A larger proportion of wall supporters, meanwhile, believe Trump should not give ground. Fifty-two percent of those who back the project think the president should demand money even if the shutdown drags on, while 41 percent believe he should compromise.
Trump has shown no willingness to give up his demand. Speaking to reporters on the White House lawn Monday, he said he rejected a suggestion from Sen. Lindsey Graham, R-S.C., to reopen the government while border security talks continue. Democratic leaders have urged him to take that path.
"I want to get it solved, I don't want to just delay it," he said. He also claimed Democrats in Congress are "stopping a lot of great people from getting paid."
Sixty-three percent of voters — including 39 percent of Republicans — support the House Democratic plan to fund most of the government through September and the Department of Homeland Security into February while wall negotiations continue.
Meanwhile, Trump has publicly mulled declaring a national emergency to build the wall without congressional approval. While some Republicans have urged him to take the action, other GOP lawmakers have said the move would set a damaging precedent and face immediate legal challenges from Democrats.
On Monday, the president claimed he has "the absolute legal right" to declare an emergency but said he is "not looking to do that" because it is "too simple."
About two-thirds, or 65 percent, of voters oppose the president using emergency powers to fund the wall.
Subscribe to CNBC on YouTube.